Simply put yes it will work, and the router doesn't need to be outdoor type. I would strongly suggest the tote be opaque as if it is clear the case of your router might melt a bit!! Don't ask how I know (experance is a great teacher). That said the router still works just fine using it now!!
Now to will it work, well hosting at a SP, the Host site about 70' up the hill had working Broadband our site didn't. So I placed my router in a clear tote at their pedestal and the WiFi worked great all the time we were there.
I no longer string cable into the camper, router stays in a tote next to the 5er. It runs our laptops and wireless printer no issues.